This is my page for my NPTEL video course that was recorded during my Fall 2010 lectures to a live class. You are expected to solve the problem sets as suggested below. No solutions are provided as they are almost always discussed during the later lectures. So it is better to try to solve the problem sets even if you can't get the correct solution.
Prerequisites  Syllabus and References  All Problem Sets as one pdf file 
A request: If you find errors in any of the lectures, send an
email to suresh.govindarajan at gmail.com pointing out the error along with
the lecture number and time on the video. Please accept my apologies for the errors which are (hopefully) of a minor nature.
Credits: The table of contents for the lectures have been provided by Naveen S. P., S. Sivaramakrishnan and T. Srinidhi who attended the live lectures. The following have pointed out errors in the lectures: Sayani Chatterjee, S. Sivaramakrishnan, Arun K. J.
I have put up twelve assignments, one quiz and one final examination (as pdf files). It is not optional but a MUST that you do the assignments as indicated below.^{1} Other supporting material (handouts, links) will be added soon! Please be patient.
Table of Contents

Module 1: Introduction to Classical Field Theory (1 Lecture)
Date  Lecture Number  Content of the Lecture  Additional Info 

Aug. 05, 2010  Lecture 1: What is Classical Field Theory?  Review of classical mechanics, Particle Trajectories and the Principle of least action, Feynman's description of QM, Classical Mechanics to Classical Fields.  Do Problem Set 1 before viewing Lecture 2! 
Module 2: Symmetries and Group Theory (6 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Aug. 09, 2010  Lecture 2: Symmetries and Invariances  I  Symmetries, Invariances of Newton's EOM vs Maxwell's Equations, The Galilean Group.  
Aug. 12, 2010  Lecture 3: Symmetries and Invariances  II  Invariances of Maxwell's Equations continued, Common Four Vectors, Covariant Formulation of Maxwell's Equations,Lorentz and Poincare Groups, Rotation Group and vectors under rotation.  Attempt Problem Set 2 after viewing Lecs. 2 and 3. 
Aug. 13, 2010  Lecture 4: Group Theory in Physics  I  Definition of a Group, Antisymmetric Matrices and $SO(d)$,Vectors and Tensors of $SO(d)$, Parity: Polar and Axial Vectors.  Solve Problem Set 3 while/after viewing lecs. 4 and 5. 
Aug. 16, 2010  Lecture 5 Group Theory in Physics  II  Generalizations of $SO(d)$ (specifically the Lorentz Group),Simple Boost Matrices and Rapidity, $SO(p,q)$ with general signatures in metric,The Symplectic Group.  40:30 The matrix should be symmetric and nondegenerate. Symplectic matrices have det=1 
Aug. 16, 2010  Lecture 6: Finite Groups  I  Finite Groups of low order : Cyclic and Coxeter(specifically Dihedral) Groups,Definition of a Subgroup, Equivalence relation and Cosets.  49:19 Left coset wrongly called right coset. Corrected at the start of lec. 7 
Aug. 19, 2010  Lecture 7: Finite Groups  II  Left and Right Cosets, Permutation Group,Normal Subgroups, Classification of Finite Simple Groups, Monstrous moonshine.  Solve Problem Set 4 while/after viewing lecs. 6 and 7. Normal Subgroups 
My colleague, Prof. Balakrishnan has given three lectures(Lec 1) on group theory as a part of his NPTEL Mathematical Physics course. You can use these lectures as a supplement to my lectures if you wish.
Module 3 Actions for Classical Field Theory (3 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Aug. 20, 2010  Lecture 8: Basics of CFT  I  Classical Mechanics of Fields, Structure of the KE term in the Lagrangian density, the ultralocal term, and Lorentz invariance of the Lagrangian.  Solve Problem Set 5 after viewing lecs. 8 and 9. 
Aug. 26, 2010  Lecture 9: Basics of CFT  II  Action Principle for fields, Conditions on Lagrangian density for no surface contribution, Conserved Currents,Hamiltonian density, Conditions for Finite Energy.  at 50:46 and 51:33 min[finite energy cond — wrong power] 
Aug. 27, 2010  Lecture 10: Basics of CFT  III  Definition of Vacuum and examples, Vacuum Solutions for quartic potential, Topological Currents and Charges, Noether's Theorem, Application to translational invariance.  Solve Problem Set 6 after viewing lec. 10 but before lec. 15 where it is discussed. 
Module 4 Green Functions for the KleinGordon Operator (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Aug. 30, 2010  Lecture 11 Green Functions  I  Inhomogenous KleinGordon Equation, Method of the Green functions, Advanced and Retarded Green Functions.  Handout on Green Functions 
Aug. 30, 2010  Lecture 12 Green Functions  II  Green Functions of the KG operator, Closing the contour,The Feynman propagator.  There are some errors. See handout. 
My colleague, Prof. Balakrishnan discusses the Green function for several families of operators as a part of his NPTEL Mathematical Physics course. You can use these lectures as a supplement to my lectures if you wish.
Module 5 Symmetries and Conserved quantities (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Sept. 09, 2010  Lecture 13 Noether's Theorem  I  Types of Symmetries, Internal Symmetries, Notion of "small", Transformations to first order (for Lorentz Group), Formulation to derive the Master formula.  21:00 Cleaner proof of antisymmetry of infinitesimal Lorentz transformations 
Sept. 06, 2010  Lecture 14 Noether's Theorem  II  Derivation of the Master formula for the Noether current, The energymomentum tensor and the generalized angular momentum tensor as examples.  Solve Problem Set 7 after viewing lec. 14 but before lec. 20 where it is discussed. 
Module 6 Solitons  I (Kink soliton) (1 lecture)
Date  Lecture Number  Content of the Lecture  Additional Info 

Sept. 06, 2010  Lecture 15 Kink Soliton  Studying timeindependent, finite energy solutions to the EulerLagrange equations of motion,the kink soliton, Derrick's theorem and its proof. 
Module 7 Hidden Symmetry (Spontaneous Symmetry Breaking) & the abelian Higgs mechanism (3 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Sept. 09, 2010  Lecture 16: Hidden Symmetry  Spontaneous symmetry breaking and statement of Goldstone's theorem.  
Sept. 13, 2010  Lecture 17: Local Symmetries  Symmetry breaking continued, The MerminWagnerColeman theorem,The ideas of global and local symmetries, the covariant derivative,Minimal prescription for the covariant derivative.  23:13 Should change the location of the minus sign in the $SO(2)$ matrix or equivalently take $q$ to $q$. 
Sept. 13, 2010  Lecture 18 The Abelian Higgs model  Definition of field strength using the covariant derivative, Small fluctuations about the vacuum solution,The Higgs mechanism in the $U(1)$ case  29:25: Index mismatch in cov. current $\mu$/$\nu$ on LHS/RHS. 
Module 8 Lie algebras, symmetry breaking and Noether's theorem for Maxwell Equations (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Sept. 16, 2010  Lecture 19: Lie Algebras  I  Recap of symmetries and Noether's theorem, Lie algebras and finitedimensional representations, $su(2)$ Lie Algebra.  Solve Problem Set 8 while viewing lectures 19/20. 
Sept. 17, 2010  Lecture 20 Lie Algebras  II  $su(3)$ Lie Algebra ; Symmetry breaking in terms of Lie algebras, Conserved currents for the Proca action: energymomentum, generalized angular momentum and the symmetric energymomentum tensors.  Equivalences of Lie algebras 
Module 9 Solitons — II (Magnetic Vortices) (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Sept. 27, 2010  Lecture 21: Magnetic Vortices  I  Finite energy, timeindependent solutions in the Abelian Higgs model in 2+1 dimensions, Topological charge == Magnetic flux, Quantization of magnetic flux, The Bogomol'nyiPrasadSommerfield(BPS) bound for energy, Saturation of the BPS bound.  Solve Problem Set 9 before viewing lecture 30. 
Oct. 04, 2010  Lecture 22: Magnetic Vortices  II  Vortices in the Abelian Higgs model applied to superconducting materials,characteristic lengths in the problem, "size" of a vortex, Description of vortex number using the fundamental group of the gauge group $U(1)$, or the circle.  35:38 and 36:03 min[finite energy cond — wrong power] 
Module 10 Towards Nonabelian gauge theories (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Oct. 07, 2010  Lecture 23: Nonabelian gauge theories  I  Nonabelian gauge symmetry with SU(2) as an example, Covariant derivative in the nonabelian case, Construction of a locally SU(2) invariant Lagrangian, Transformation of the gauge fields under local gauge transformations.  Solve Problem Set 10 while viewing lectures 23/24. 
Oct. 08, 2010  Lecture 24: Nonabelian gauge theories  II  Transformation of the gauge fields(continued), Derivation of the field strength for the gauge field, Symmetry breaking in the nonabelian case, Goldstone's theorem in terms of Lie Algebras. 
Module 11 Representation theory of Lie Algebras (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Oct. 11, 2010  Lecture 25: Irreps of Lie algebras  I  Representation theory of $su(2)$ and $su(3)$, the Cartan subalgebra, the adjoint representation.  3:00  Misleading statement: Map from G to GL(N). While GL(N) is set of all linear maps on V, the map from G to GL(N) is not linear.28:00  Blocks "0" and "*" in the matrix have been interchanged. 
Oct. 14, 2010  Lecture 26: Irreps of Lie algebras  II  Representation theory continued, Ferrer's diagrams. 
Quiz (Test yourself)
If you have gotten this far, you can test you understanding by taking this Quiz. It is meant to be an open notes (i.e., your own notes) examination and the expected duration is one and half hours. I don't intend to post the solutions online but they will be provided on request. This is to counter the natural human tendency to look at solutions if they are available! What is a good score? I would say anything over 50% is acceptable.
Module 12 The Standard Model of Particle Physics (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Oct. 15, 2010  Lecture 27 The Standard Model  I  $su(3)$ multiplets, Motivation for the Standard Model, Colour confinement, GellMann—Nishijima relation.  
Oct. 18, 2010  Lecture 28 The Standard Model  II  Electroweak symmetry breaking — An application of symmetry breaking in the nonabelian case.  Typo towards the end: The prediction is that there is a massive (not massless) particle. 
Module 13 The Lorentz and Poincare Lie Algebras (1 Lecture)
Date  Lecture Number  Content of the Lecture  Additional Info 

Oct. 21, 2010  Lecture 29: Irreps of the Lorentz/Poincare algebras  The Lorentz and Poincare algebras and their representations. 
Module 14 Solitons — III (Monopoles and Dyons) (3 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Oct. 22, 2010  Lecture 30: The Dirac mononpole  Magnetically charged solutions: The Dirac monopole, Flux quantization.  Solve Problem Set 11 while viewing lectures 30/31/32. 
Oct. 25, 2010  Lecture 31: The 't HooftPolaykov monopole  Magnetically charged solutions: The ‘t HooftPolyakov monopole, The PrasadSommerfield limit.  
Oct. 28, 2010  Lecture 32: Revisiting Derrick’s Theorem  Revisiting Derrick's theorem, BPS solution  
Nov. 1, 2010  Lecture 33: The JuliaZee dyon  Constructing dyonic solutions, Dirac quantization for dyons; Dimensional reduction. 
Module 15 Instantons and their physical interpretation (4 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Nov. 4, 2010  Lecture 34: Instantons  I  Quantum mechanical tunnelling and Instantons.  Solve Problem Set 12 while viewing lectures 34/37. 
Nov. 8, 2010  Lecture 35: Instantons  II  Kink soliton and tunnelling, Instantons in pure YangMills theories(SU(2)).  
Nov. 11, 2010  Lecture 36:  Instantons  III  More on instantons, The BPS bound.  
Nov. 12, 2010  Lecture 37: Instantons  IV  Free parameters in instanton solutions, moduli space, Complexified YangMills and theta vacua. 
Module 16 An introduction to some advanced topics (2 Lectures)
Date  Lecture Number  Content of the Lecture  Additional Info 

Nov. 15, 2010  Lecture 38: Dualities  Dualities in Field Theory: Ising Model; SineGordon / Massive Thirring; SU(2) YangMills in 3+1 dimensions.  
Nov. 18, 2010  Lecture 39: Geometrization of Field Theory  General relativity as a gauge theory; Geometrization of Field Theory; Glimpse into String theory and branes. 
The Final
If you have gotten this far, you can test your understanding (of the course material) by taking this Final Examination. It is meant to be an open notes (i.e., your own notes) examination and the expected duration is three hours. I don't intend to post the solutions online but they will be provided on request.